Solutions of uniform, open-channel, liquid metal flow in a strong, oblique magnetic field

Abstract

The flow of an electrically conducting fluid in an open channel in the presence of a strong magnetic field of oblique incidence to both the channel walls and the force of gravity is explored. This type of flow has possible applications to the protection of high heat flux surfaces in magnetic confinement fusion reactors. The governing equations of fully-developed flow are derived retaining all viscous terms. They are then solved in the strong field limit in an asymptotic, iterative fashion, carrying the first two terms in the expansion with powers of the effective Hartmann number. The asymptotic solutions for the velocity, induced magnetic field and the flow rate are compared with a numerical solution of the complete governing equations. Good agreement is seen between the asymptotic and numerical predictions of velocity and electric current distribution when the core regions are dominated by magnetic forces. One novel feature of open channel flow of this type is the existence, predicted by the asymptotic analysis and confirmed by the numerical integration, of a second-order Hartmann layer on the free surface. Its presence is required to ensure the condition of no shear stress on this boundary. Also seen is the presence of strong discontinuities across free shear layers, which form along the field lines that extend from the free surface/sidewall corner.